A165825 Totally multiplicative sequence with a(p) = 4.

1, 4, 4, 16, 4, 16, 4, 64, 16, 16, 4, 64, 4, 16, 16, 256, 4, 64, 4, 64, 16, 16, 4, 256, 16, 16, 64, 64, 4, 64, 4, 1024, 16, 16, 16, 256, 4, 16, 16, 256, 4, 64, 4, 64, 64, 16, 4, 1024, 16, 64

Offset: 1

Author

Jaroslav Krizek, Sep 28 2009

Keywords

• nonn
• mult

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000302, A001222, A061142, A165824, A351521.

Programs

Mathematica

4^PrimeOmega[Range[100]] (* G. C. Greubel, Apr 09 2016 *)

PARI

a(n) = 4^bigomega(n); \\ Altug Alkan, Apr 09 2016

PARI

for(n=1, 100, print1(direuler(p=2, n, 1/(1 - 4*X))[n], ", ")) \\ Vaclav Kotesovec, Feb 17 2022

Formula

a(n) = A000302(A001222(n)) = 4^bigomega(n) = 4^A001222(n).

Dirichlet g.f.: Product_{p prime} 1 / (1 - 4 * p^(-s)). - Ilya Gutkovskiy, Oct 30 2019

Sum_{k=1..n} a(k) = c * n^2 / (2 * log(2)) + O(n * log(n)^3), where c = Product_{p prime > 2} 1 / (1 - 4/p^2) = 2.6413142332392629671869467536904049315527375203817456105081927074458279809... - Vaclav Kotesovec, Feb 17 2022